Devil May Cry 1&3
Resident Evil 4 (if you don't have a Wii)
God of war 1&2
Zone of the Enders 2
GranTurismo 4 with steering wheel
Burnout 3 to release some steam after GT
MetalGearSolid 3
Final fantasy XII
Kingdom Hearts I&II (if you have nothing against fighting with Disney characters)

Oh and DeadOrAlive2 you can get it for close to nothing, and it's so good in multiplayer!

I wanted to add so many more games... But then I thought those up there are the ones I consider "essentials", if you don't have them, and you have a PS2, you're from another planet.
The others would be more games I really really enjoyed, but there "essentiallity" is questionable...

In their own little space since they're Japanese SHMUPs but worth checking out!
Espgaluda
Ibara
Mushi-Hime Sama

And although they won't appeal to most people being a big music game fan I also enjoy:
DDR 6th/7th/Extreme (Jp), MAX, MAX 2, Extreme, Suprnova (US)
In the Groove
ParaParaParadise
Pop'N Music 7-14
Taiko Drum Master (10+ games)
Singstar (10+ games) (Better than karaoke Revolution)